Finite state machines and pushdown systems are frequently used in model based testing. In such testing, the system under test is abstractly modeled as a finite state machine having a finite set of states and a labeled transition relation between the states. A pushdown system, additionally, has an unbounded stack. Test inputs are then generated by enumerating a set of sequences of transitions labels from the model. There has been a lot of research that focused on generation of test input sequences satisfying various coverage criteria.